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\int\frac{2x-1}{\left(x-1\right)\left(x-2\right)\left(2x-3\right)}dx

Integral of (2x-1)/((x-2)(2x-3)*(x-1))

Answer

$-4\ln\left|2x-3\right|+3\ln\left|x-2\right|+\ln\left|x-1\right|+C_0$

Step-by-step explanation

Problem

$\int\frac{2x-1}{\left(x-1\right)\left(x-2\right)\left(2x-3\right)}dx$
1

Using partial fraction decomposition, the fraction $\frac{2x-1}{\left(2x-3\right)\left(x-2\right)\left(x-1\right)}$ can be rewritten as

$\frac{2x-1}{\left(2x-3\right)\left(x-2\right)\left(x-1\right)}=\frac{A}{2x-3}+\frac{B}{x-2}+\frac{C}{x-1}$

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Answer

$-4\ln\left|2x-3\right|+3\ln\left|x-2\right|+\ln\left|x-1\right|+C_0$
$\int\frac{2x-1}{\left(x-1\right)\left(x-2\right)\left(2x-3\right)}dx$

Main topic:

Integrals by partial fraction expansion

Used formulas:

4. See formulas

Time to solve it:

0.94 seconds